Problem 15 - Chemistry

Question

Calculate \(w,\) and determine whether work is done \(b y\) the system or on the system when \(415 \mathrm{~J}\) of heat is released and \(\Delta U=510 \mathrm{~J} .\)

Step-by-Step Solution

Answer

Work done is -925 J; it is done on the system.

Step 1: Understand the First Law of Thermodynamics

The First Law of Thermodynamics is given by the formula \( \Delta U = Q - W \), where \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to or released from the system, and \( W \) is the work done by the system. Our task is to find \( W \) when \( Q = -415 \text{ J} \) (since 415 J of heat is released, making it negative in the formula) and \( \Delta U = 510 \text{ J} \).

Step 2: Rearrange the formula to solve for work (W)

We need to find the work (\( W \)) using the rearranged formula: \( W = Q - \Delta U \).

Step 3: Substitute the values into the equation

Substitute \( Q = -415 \text{ J} \) and \( \Delta U = 510 \text{ J} \) into the formula: \[W = (-415) - 510\].

Step 4: Calculate the work (W)

Perform the calculation from the equation:\[W = -415 - 510 = -925 \text{ J}\]. The negative sign indicates that work is done on the system.

Key Concepts

Understanding Internal Energy

Internal energy is a central concept in thermodynamics which represents the total energy contained within a system. It accounts for the microscopic energy due to molecular motion and interactions. When we discuss internal energy, we are referring to any non-mechanical energy. In the First Law of Thermodynamics, the change in internal energy, denoted by \( \Delta U \), is an important parameter.

For example, if a system has \( \Delta U = 510 \text{ J} \), this increase indicates that the system has absorbed energy in some form. Whether from heat transfer, work, or both, an increase in internal energy means that the particles inside the system have more energy. This could result in increased vibration, rotation, or other forms of movement at the molecular level. Being able to calculate and understand changes in internal energy is fundamental in explaining how energy exchanges occur within a system.

The Role of Heat Transfer

Heat transfer plays a critical role in changing the energy state of a system. It refers to the heat flowing into or out of a system. In thermodynamics, heat is represented by \( Q \). A positive \( Q \) indicates heat added to the system, while a negative \( Q \) means heat is released from the system.

For instance, in the given exercise, \( Q = -415 \text{ J} \) implies that the system is releasing 415 joules of energy as heat. This will, in turn, affect the internal energy and potentially the type and amount of work the system does. Understanding heat transfer helps in predicting how a system's total energy will vary and is a critical step in applying the First Law of Thermodynamics effectively. Mastering this concept is key to controlling energy appliances and processes, where energy efficiency and control are crucial.

Work Done by the System versus Work Done on the System

In thermodynamics, analyzing work is crucial for understanding energy exchanges. The term "work" refers to the energy transfer when a force is applied over a distance. In terms of the First Law of Thermodynamics, work done by the system (\( W \)) can be positive when energy leaves the system, and negative when energy enters.

In the exercise, the calculation \( W = -925 \text{ J} \) signifies work is done on the system. Imagine physically compressing a piston; this negative work results in the system gaining energy. This opposes the work done by the system, often seen if systems like engines powerfully push pistons outward. Through analyzing whether work is done by or on the system, energy transfer processes in engines, refrigerators, and other thermodynamic devices can be understood and optimized more effectively.